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22 August, 02:55

Claire spent $450 of her allowance each month and saved the rest. If she increased her spending by 18% her savings would decrease by 30%. How much was her monthly allowance?

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  1. 22 August, 03:00
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    Answer: her monthly allowance is $630

    Step-by-step explanation:

    Let x represent her monthly allowance.

    Claire spent $450 of her allowance each month and saved the rest. This means that the amount she saved each month is x - 450

    If she increased her spending by 18% her savings would decrease by 30%. The expression for an 18% increase in her spending would be

    (18/100 * 450) + 450 = 81 + 450

    = 531

    The expression for a 30% decrease in her savings would be

    (x - 45) - [30/100 * (x - 450) ]

    = (x - 45) - [0.3 (x - 450) ]

    = (x - 45) - [0.3x - 135]

    = x - 45 - 0.3x + 135

    = x - 0.3x - 45 + 135

    = 0.7x + 90

    Therefore,

    0.7x + 90 = 531

    0.7x = 531 - 90

    0.7x = 441

    x = 441/0.7

    x = $630
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